Mathematical Modeling and Numerical Simulation of Thermal Ablation Treatments in Heart Arrhythmias
Catheter ablation is a procedure that is used to treat cardiovascular diseases, specially arrhythmias. A catheter, that is inserted through a vein, is placed in the affected area of the heart, and an electric shock is applied in order to destroy the abnormal tissue. If the temperature of the cardiac...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | español |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/14418 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/14418 |
| Access Level: | acceso abierto |
| Palabra clave: | 616.12-008.318 519.87 Arrhythmia Catheter ablation Cardiac tissue Temperature distribution Arritmias Ablación cardíaca Matemática aplicada Física-Modelos matemáticos Física matemática Análisis numérico Ecuaciones diferenciales Cardiología 1206 Análisis Numérico 1202.07 Ecuaciones en Diferencias 3205.01 Cardiología |
| Sumario: | Catheter ablation is a procedure that is used to treat cardiovascular diseases, specially arrhythmias. A catheter, that is inserted through a vein, is placed in the affected area of the heart, and an electric shock is applied in order to destroy the abnormal tissue. If the temperature of the cardiac tissue exceds a certain threshold stream pops occur, and this phenomenon can lead to serious complications. Therefore, a very helpful aspect consists of obtaining the temperature distribution in the cardiac tissue. The number of studies centered in the mathematical modelization of the problem is limited, and the existing ones lack important sections as numerical scheme validations or certain correlation justifications. This is the reason why it is necessary to extend the preceding studies, the objective being to obtain results as realistic as possible. Taking into account the previous remarks, the main goal of this work is to take a first step towards analising the problem, considering a simple three-dimensional model; in particular, assuming rotational symmetry and approximating blood velocity by mean values. Moreover, making additional simplifications the problem can be reduced to a system of two parabolic equations and two elliptic equations, both of them subjected to compatibility conditions. The system is solved numerically by means of a spectral method. With respect to the results, the temperature values that are obtained in standard conditions are coherent. Furthermore, a parametric study of the procedure is performed, together with an assessment of the importance of several assumptions made in the model. The results section concludes with an optimal control analysis of the system. |
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